**Advances in Soviet Mathematics**

1994;
289 pp;
Hardcover

MSC: Primary 82;

Print ISBN: 978-0-8218-4120-4

Product Code: ADVSOV/20

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

**Electronic ISBN: 978-1-4704-4618-5
Product Code: ADVSOV/20.E**

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

# Probability Contributions to Statistical Mechanics

Share this page *Edited by *
*R L. Dobrushin*

Physics has always been a fertile source of new mathematical notions and ideas, and in the past decade the stream of ideas from physics to mathematics has increased dramatically. The subfield of statistical mechanics is no exception. Containing papers written by representatives of the Moscow school of mathematical statistical mechanics, this volume illustrates certain aspects of the developing interaction between statistical mechanics on the one hand and the theories of probability and of dynamical systems on the other. Included here are papers on random walks, phase transition phenomena for Gibbs random fields, the existence of nonstandard motion integrals in statistical physics models, and the Frenkel-Kontorova model.

#### Readership

Graduate students and researchers in mathematics and statistical physics.

# Table of Contents

## Probability Contributions to Statistical Mechanics

- Cover Cover11
- Title page v6
- Contents vii8
- Foreword ix10
- An extension of the Ising model 114
- Central limit theorem for the random walk of one and two particles in a random environment, with mutual interaction 2134
- Random walk of a particle interacting with a random field 7790
- Large and moderate deviations in the Ising model 91104
- Asymptotically additive integrals of motion for particles with nonpairwise interaction in dimension one 221234
- On a ground state in the Frenkel-Kontorova model and metric properties of mappings of standard type 277290
- Back Cover Back Cover1304